Khovanov homology and exotic surfaces in the 4-ball
K Hayden, I Sundberg - Journal für die reine und angewandte …, 2024 - degruyter.com
We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces
in the 4-ball that are exotically knotted (ie, isotopic through ambient homeomorphisms but …
in the 4-ball that are exotically knotted (ie, isotopic through ambient homeomorphisms but …
Invariants of 4-manifolds from Khovanov-Rozansky link homology
S Morrison, K Walker, P Wedrich - Geom. Topol, 2022 - msp.org
Following the seminal articles of Jones, Witten and Atiyah [38; 86; 3], Crane and Frenkel
outlined their vision for an algebraic construction of invariants of smooth 4–dimensional …
outlined their vision for an algebraic construction of invariants of smooth 4–dimensional …
Kirby belts, categorified projectors, and the skein lasagna module of s2× S2
IA Sullivan, M Zhang - arXiv preprint arXiv:2402.01081, 2024 - ems.press
We interpret Manolescu–Neithalath's cabled Khovanov homology formula for computing
Morrison–Walker–Wedrich's KhR2 skein lasagna module as a homotopy colimit (mapping …
Morrison–Walker–Wedrich's KhR2 skein lasagna module as a homotopy colimit (mapping …
A Kirby color for Khovanov homology
We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular
Bar-Natan category that is equipped with a natural handle slide isomorphism. Using …
Bar-Natan category that is equipped with a natural handle slide isomorphism. Using …
[PDF][PDF] A braided monoidal (∞, 2)-category of Soergel bimodules
YL Liu, A Mazel-Gee, D Reutter… - arXiv preprint arXiv …, 2024 - math.uni-bonn.de
The Hecke algebras for all symmetric groups taken together form a braided monoidal
category that controls all quantum link invariants of type A and, by extension, the standard …
category that controls all quantum link invariants of type A and, by extension, the standard …
Khovanov homology and exotic -manifolds
Q Ren, M Willis - arXiv preprint arXiv:2402.10452, 2024 - arxiv.org
We show that the Khovanov-Rozansky $\mathfrak {gl} _2 $ skein lasagna module
distinguishes the exotic pair of knot traces $ X_ {-1}(-5_2) $ and $ X_ {-1}(P (3,-3,-8)) $, an …
distinguishes the exotic pair of knot traces $ X_ {-1}(-5_2) $ and $ X_ {-1}(P (3,-3,-8)) $, an …
Invariants of surfaces in smooth 4-manifolds from link homology
S Morrison, K Walker, P Wedrich - arXiv preprint arXiv:2401.06600, 2024 - arxiv.org
We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for
links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna …
links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna …
Bordered invariants from Khovanov homology
To every compact oriented surface that is composed entirely out of 2-dimensional 0-and 1-
handles, we construct a dg category using structures arising in Khovanov homology. These …
handles, we construct a dg category using structures arising in Khovanov homology. These …
Notes on Khovanov homology
M Zhang - arXiv preprint arXiv:2501.03115, 2025 - arxiv.org
These are expository lecture notes from a graduate topics course taught by the author on
Khovanov homology and related invariants. Major topics include the Jones polynomial …
Khovanov homology and related invariants. Major topics include the Jones polynomial …